论文标题
生成局部符号类固醇和非扰动半经典量化的功能
Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization
论文作者
论文摘要
本文包含三个有关生成泊松括号的谎言理论整合及其与量化关系的结果。在首先，我们展示了如何构建与任何局部符号群体的细菌相关的生成函数，并提供明确的（平滑，非正式）通用公式$s_π$用于在坐标空间上集成任何泊松结构$π$。第二个结果涉及与半经典量化的关系。我们表明，$ s_ {tπ} $的正式taylor扩展在$ t = 0 $上获得了基于树皮的Kontsevich的Star产品配方的提取物，从[6]中恢复了Cattaneo，Dherin和Felder引入的正式家庭。第三个结果涉及与泊松西格玛模型的半经典方面的关系。我们表明，$s_π$可以通过非扰动功能方法获得，评估在磁盘上PDE解决方案族的某个功能，为此我们显示存在和分类。
This paper contains three results about generating functions for Lie-theoretic integration of Poisson brackets and their relation to quantization. In the first, we show how to construct a generating function associated to the germ of any local symplectic groupoid and we provide an explicit (smooth, non-formal) universal formula $S_π$ for integrating any Poisson structure $π$ on a coordinate space. The second result involves the relation to semiclassical quantization. We show that the formal Taylor expansion of $S_{tπ}$ around $t=0$ yields an extract of Kontsevich's star product formula based on tree-graphs, recovering the formal family introduced by Cattaneo, Dherin and Felder in [6]. The third result involves the relation to semiclassical aspects of the Poisson Sigma model. We show that $S_π$ can be obtained by non-perturbative functional methods, evaluating a certain functional on families of solutions of a PDE on a disk, for which we show existence and classification.
